OK So adding a few things for posterity:
Driver board works! I have a dead IC channel (woops) but I can fix that. Elimination of the cat from the workspace was really valuable!
1) The amount of time needed (I.E. Current) is actually pretty low. not sure how to measure core saturation, if someone has any ideas, I'd love to hear them! I'd like to tune current pulse time to something pretty low. Bottom line, average voltage is about 14v for 2ms,
2) Here's a scope trace of my the supply voltage at 15V. This is adding ~3000uF worth of caps to the circuit!
The flip time is about 2ms as you can see from the current downswing to 13V (defined in my microcontroller as just a timer variable in ms, as sending the SPI commands is about ~30us) and it flips dots nicely - I bet it could go much lower in time, extra time sent to the coil actually seems counterproductive (overmagnetizing core? I dunno man)
3) It takes 5ms to charge the caps (the swing back to 15V) after a flip. Reducing "on" time will help reduce how much capacitor charge time I need - any thoughts on what kind of components I can use to improve this?